Unlike the brilliant anime, the Death Note manga in my opinions isn't quite as good. Yes, the story-line is identical apart froma few minor differences, nothing that changes anything. If you've seen the anime, you'll find it tedious re-reading the manga. Its the same.
However Death Note doesn't quite suit the manga as well as the anime. It starts of very good, but towards the later numbers it becomes heavily text-based and you'll be trolling through pages of talkign which is slightly more bearable in anime.
The only down-side to the manga is the artwork. Overall it is very good, but at time if you read it, you'll notice it is a bit sloppy, L most of all looks kinda retarded at times and a lot like an ape, therefore
Overall it still is very good but just not quite up to scratch compared to the anime, I'd still recommend it as a good read.